pH Dependence of the Electron-Transfer Coefficient: Comparing a

Article pubs.acs.org/JPCC

pH Dependence of the Electron-Transfer Coefficient: Comparing a Model to Experiment for Hydrogen Evolution Reaction Shima Haghighat and Jahan M. Dawlaty* Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States S Supporting Information *

ABSTRACT: The empirical electron-transfer coefficient α is a valuable electrochemical observable that bridges the thermodynamics and kinetics of redox reactions. For reactions that involve protons, the value of α is expected to be pHdependent. However, even for the simplest redox processes, the nature of this dependency remains unclear. Toward clarifying this problem, we follow two goals. First, we calculate the electron-transfer coefficient α and its pH dependence based on a model 2D potential energy surface that has been investigated by Koper and Schmickler for proton reduction. According to the model, α is pH-independent for high-pH values and pH-dependent for low-pH values, with α increasing as the pH is lowered. Second, we report our experimentally measured α for hydrogen evolution on several electrode materials over a wide pH range. We observe that several features of the data show similarities to the predictions of the model. The data show different behavior in two distinct pH regions. In the acidic region, a linearly increasing α with decreasing pH and in the basic side a pH-independent α are observed for several electrodes. However, certain predictions of the model, in particular the transition pH between the two regions, do not seem consistent with the data, which we propose likely arises due to mass-transfer limitations of the rate. We hope that this work will help better understand the pH dependence of interfacial electron−proton transfer reactions and, in particular, inspire further work to isolate mass-transfer limitations from interfacial chemistry effects in measuring and interpreting the electron-transfer coefficient.

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INTRODUCTION The electron-transfer coefficient α is a fundamental electrochemical observable. It is formally defined as the rate of change of the activation barrier ΔG‡ with respect to the thermodynamic drive ΔG for a reaction α = ∂ΔG‡/∂ΔG.1−3 The thermodynamic drive is determined by the externally controlled potential E as ΔG = −F E, and, assuming the usual Arrhenius process, the empirical α may be inferred from the experimentally determined current I and potential E as α = −(2.3RT/F)(∂ log I/∂E) for a reduction reaction. Thus α is a measure of the sensitivity of the kinetics to the thermodynamic drive. If and when it is assumed constant, it is the coefficient for the commonly known linear free-energy relationship ΔG‡ = b + αΔG. Both the thermodynamics and kinetics of proton-requiring reactions are sensitive to the chemical potential of protons. Therefore, the electron-transfer coefficient is expected to be pH-dependent. Despite decades of research on this front, the details of this dependency remain obscure, even for the simplest of the redox reactions.4−6 The heterogeneous hydrogen evolution reaction (HER) 2H+ + 2e− → H2 is arguably both a scientifically fundamental and nowadays a technologically relevant process. In particular, the reduction of a single proton by one electron that results in an adsorbed hydrogen atom on the surface (the Volmer reaction) is sometimes implicated as rate-limiting for HER.5,7,8 A large number of questions remain © XXXX American Chemical Society

unanswered about HER. Although preparing new catalysts for HER has been an active field in materials chemistry,6,9−14 often new catalysts are tested only in the low-pH region for better performance.15−18 When the pH dependence of reaction rates is studied, often nontrivial dependence is reported over a large pH range.5,19−22 It is usually unclear whether the chemical aspects of the reaction (e.g., barriers for proton transfer near the surface) or the mass transport limitations influence the rate. The details of the electrolyte, for example, buffer equilibria, often influence the rates in nontrivial ways, and a consistent picture does not seem to exist. Finally, because of the complexity of surface spectroscopy compared with bulk measurements, much less is known about heterogeneous reactions and electrolyte properties near the surface. In this work, we have two goals. First, we analyze a parametrized potential energy surface (PES) for the reduction of one proton (Volmer reaction) that is based on the work of Schmickler23,24 and Koper.25,26 The PES is constructed in two dimensions corresponding to proton and electron transfer and allows for both concerted proton−electron transfer (CPET) and stepwise transfer through intermediates. An advantage of this approach is that the influence of pH on the geometry of the Received: October 20, 2016 Revised: November 30, 2016 Published: November 30, 2016 A

DOI: 10.1021/acs.jpcc.6b10602 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

current to 0.1 mA and ignored the regions of low overpotential where the current is too low for a derivative to be meaningful. Also, to evaluate the average value of α for each electrode material at each pH value, we calculated the average value of α over a range of 50 mV right after the onset current (0.1 mA). The error in the value of α depends on several parameters, including the value of current at which α is measured. Our average estimate for the error in α is in the order of 0.05. For the rotating disk electrode (RDE) measurements, we used platinum, gold, and glassy carbon RDEs (Gamry-E6 Series) all with surface area of 0.196 cm2.

PES and consequently on the reaction path can be conveniently accounted for. After stating the structure of the model, we compute the pH dependence of the electron-transfer coefficient α at low- and high-pH limits. We arrive at distinctly different results for the two limits. Our second goal is presenting experimental results that show the variation of α for hydrogen evolution on several types of electrodes over a wide pH range. In particular, we use a 2D representation27,28 to draw attention to the variation of α as a function of both pH and potential. We point out the stark difference between the pH dependence of α in the high- and low-pH limits. We also comment on how mass-transfer limitations influence experimental determination of α. Finally, we will compare the experimental results to the trends that are inferred from the model. We show that several experimental trends and behaviors have similarities to the predictions of the models. This includes the distinctly different behavior of α in the low- and high-pH limits. However, we also show that several features in the data are not explainable by the model. We suggest that a possible origin for the inconsistency is the inadequacy of the experimental methods in fully isolating mass-transfer limitations on the electrochemical current. We believe that this work will encourage further theoretical and experimental work to better understand the mechanism of proton-requiring redox reactions. In particular, further theoretical explorations of the 2D PES are necessary, with attention to relating the PES to experimental observables. On the experimental front, methods that will better isolate masstransfer effects and methods to measure surface properties locally are desired.

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FOUR-STATE POTENTIAL ENERGY SURFACE FOR PROTON REDUCTION Schmickler and Koper have worked on a 2D PES for the electrochemical electron−proton transfer and, in particular, the proton reduction reaction.23−26 Other models for the electrochemical electron−proton transfer also exist and have their own value.29−32 We will use the Schmickler−Koper approach since it introduces experimentally controllable parameters into the model in a convenient way. We will calculate electron-transfer coefficients based on this model. For notational consistency, and in particular to emphasize the influence of pH on reaction paths, we will briefly introduce the model. Then, we will proceed with identifying the stepwise and concerted limits of proton transfer according to this model and calculating their respective electron-transfer coefficients. We consider the influence of pH and potential on the thermodynamics of the Volmer reaction.

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M + H+ + e− → MH

METHODS Electrochemical data were obtained using a Gamry Reference 3000 potentiostat and a three-electrode cell. A Ag/AgCl reference electrode (Ag/AgCl vs NHE = +197 mV) and graphite rod counter electrode were used in all of the experiments. The working electrodes were seven different materials as follows: platinum gauze (52 mesh woven with surface area of 8.3 cm2, Alfa Aesar), Ti and Ni (surface area: 1 cm2, MTI), gold (as a thin film on silicon, surface area: 1.9 cm2, LGA Thin Films) iron pyrite (FeS2) (surface area: 1.5 cm2, Geollector), copper (surface area: 1 cm2, Metalliferous), and glassy carbon (surface area: 1 cm2, Glas 11 grade, SPI supplies). The electrolyte solution was 0.1 M KCl, and its pH was adjusted by adding a dilute HCl solution. To avoid influences from the specific adsorption of multivalent anions, no agent for pH buffering was added. The cell was purged with N2 gas prior to each scan and then was closed to the ambient air. Current− voltage curves were obtained for at least 12 to 15 values of pH between pH 6.5 and 1.5. The indicated potentials are always referenced to the normal hydrogen electrode. Linear sweep voltammetry experiments were carried out at 10 mV/s scan rate between 0 and −2 V versus Ag/AgCl electrode. The resistance of the electrolyte solution and the electrodes was evaluated using a common method, as outlined by Trasatti (see Supporting Information (SI)). For completeness, the IRcompensated plots are provided in the SI. As explained in the SI, in the regions of low overpotential, the behavior of α is not significantly different for the compensated and uncompensated cases. To construct the α(pH,E) diagram, we took the gradient of the logI along the potential axes for each pH and calculated α(pH,E). In determining the derivatives, we set the onset

(1)

Here M is a surface site that catalyzes the reaction of a proton (abstracted from the electrolyte) with an electron to create chemically adsorbed hydrogen MH. The thermodynamics of this reaction is clearly a function of the electrode potential (i.e., chemical potential of electron) and the electrolyte pH (i.e., the chemical potential of protons in the electrolyte). It is conventional to consider four states for the reaction 1, as shown in Figure 1. States 1 and 4 are the reactants and

Figure 1. Four states participating in the Volmer reaction.

products, while states 2 and 3 are proton-transfer and electrontransfer intermediates. We assume the potential to be E, which is relative to an arbitrary reference. Soon we will choose the equilibrium potential as the reference. In assigning thermodynamic free energy to each one of the four states, we follow the conventional understanding of the electron and proton free energies in the electrode and in the electrolyte, respectively. The free energy of electron in the electrode is proportional to the potential E as G(e−) = −eNA E = −FE, where e is the charge of the electron and F is the Faraday constant. The free energy of solvated protons G(H+) is B


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The Journal of Physical Chemistry C related to pH via G(H+) = G0(H+) − 2.3RT pH. At pH 0, we set the G0(H+) to be zero as a reference point. Then we have G(H+) = −2.3RT pH. Thus the free energies of the four states shown in Figure 1 are G1 = −FE + G(M) − 2.3RT pH

(2)

G2 = −FE + G(MH+)

(3)

G3 = G(M−) − 2.3RT pH

(4)

G4 = G(MH)

in eqs 12−15 and quadratic increase in energy as a function of qp and qe. G1(qe , qp) = λeqe2 + λpqp2 + 2λ ̅ qeqp − Fη G2(qe , qp) =

1 (G(M) − G(MH) − 2.3RT pH ) F

G3(qe , qp) = λe(qe − 1) +

(19)

The coefficient λe is the familiar reorganization energy along the electron-transfer coordinate, and λp is the natural extension of that for proton transfer. The parameter λ̅ is referred to as the solvent overlap parameter and accounts for those types of motion in the environment that influence both electron and proton transfer. The minima corresponding to eqs 12−15 are located at {qe = qp = 0}, {qe = 0, qp = 1}, {qe = 1, qp = 0}, and {qe = qp = 1}, respectively. To construct an approximate adiabatic PES, the coupling between the diabatic surfaces near crossing points is considered strong enough to allow transitions from one to the other but weak enough such that energy splitting is minimal. Thus the approximate adiabatic free-energy surface is constructed as the minimum of the four diabatic surfaces above.

Next, we consider the protonation free energies for M and M− from the following two reactions

(9)

and define ΔGprot = G(MH+) − G(M) + 2.3RT pH

(10)

− ΔGprot = G(MH) − G(M−) + 2.3RT pH

(11)

2

G4(qe , qp) = λe(qe − 1) + λp(qp − 1) + 2λ ̅ (qe − 1)(qp − 1)

(7)

M− + H+ → MH

+ 2λ ̅ (qe − 1)qp −

− ΔGprot

(18)

(6)

(8)

λpqp2

2

(5)

M + H+ → MH+

+ λp(qp − 1) + 2λ ̅ qe(qp − 1) − Fη + ΔGprot

(17)

Using this value as a reference, we define the overpotential η as η = E − Eeq

(16)

2

2

For convenience, we find the potential that brings the reaction to equilibrium G(1) = G(4) at a given pH. Eeq =

λeqe2

G(qe , qp) = min{G1 , G2 , G3 , G4}

(20)

An example of such a surface is shown in Figure 2, with the parameters mentioned in the Figure caption. To allow smooth

Equations 7, 10, and 11 can be inserted into the free energies in eqs 2−5. Given that G(MH) is common to all energies, it is most convenient to consider relative energies and subtract it from all, leading to

G1 = −Fη

(12)

G2 = −Fη + ΔGprot

(13)

− −ΔGprot

(14)

G3 =

G4 = 0

(15)

The above is not different from what we started from (eqs 2−5). However, it is cast in a convenient way using only three intuitive quantities: the overpotential η, the protonation free energies of the neutral ΔGprot, and negatively charged ΔG−prot surface site. Next, we consider transitions between the four states described above. To describe transitions, a PES that connects these states must be constructed. Schmickler23,24 has calculated adiabatic PESs that connect the four states described above. The distance of a proton from the surface represents the proton-transfer coordinate, and the electronic charge on the surface site represents the electron-transfer coordinate. Then, the energies of the four states are smoothly connected to each other through variations along these coordinates, producing a 2D PES. The resulting surface is analogous to the Marcus electron-transfer parabolas in two dimensions, which have been discussed in the literature.31 We shall refer to the coordinate aligned with proton and electron transfer as qp and qe, respectively. Built on this, Koper25 has considered the four states as diabatic surfaces, each with a minimum energy shown

Figure 2. Example of an adiabatic potential energy surfaces of the four states as a function of electron- and proton-transfer coordinates qe and qp. The parameters employed are η = 0 V, λe = λp = 1 eV, λ̅ = 0.5 eV, ΔGprot = 0.1 eV, and ΔG−prot = −0.2 eV.

representation in the Figure, a small coupling between the surfaces is introduced. From the Figure, it is evident that the form of the PES is a function of the three parameters determining the minima of the diabatic states Fη, ΔGprot, and ΔG−prot, as shown in eqs 12−15, and the three parameters λe, λp, and λ̅ determine how the energies of the states change upon moving along the electron- and proton-transfer coordinates. Now we consider the case in which ΔG−prot is much more negative than ΔGprot. This is a likely scenario because protonation of M− is reasonably much more favorable than protonation of M. In this case, the G3(qe,qp) surface will be shifted very high, and a passage from 1 to 3 and then to 4 will not be permitted. Thus we consider transitions from 1 to 4 C


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The Journal of Physical Chemistry C either directly across the diagonal or from 1 to the proton transfer intermediate 2 and then to 4. We will refer to these as the concerted and stepwise paths, respectively. Next, we consider the influence of pH on the surface. For simplicity, we consider η = 0 and notice from eq 13 that the minimum energy of G2 is ΔGprot, which according to eq 10 depends on pH. Thus lowering the pH makes protonation of M more favorable and lowers the corner of the PES corresponding to the minimum of G2. Raising the pH, on the contrary, makes proton transfer less favorable and raises this corner. Thus the height of surface at the {qe = 0, qp = 1} corner is controlled by pH. A consequence of this observation is that for large values of pH, for which proton transfer via 2 is not favorable, the only available path for proton transfer is the concerted path through the diagonal. At the other extreme, for low-pH values, the corner corresponding to G2 is significantly lowered, and the electrode is readily protonated. The transition state, in that case, lies along the electron-transfer coordinate between G2 and G4. Following Koper, the transition state for each case can be found by first finding the crossing of the respective diabatic surfaces and then finding the point of minimum energy along that line. To begin with, we find the transition state between states 2 and 4. It is easy to show (see SI) that at the crossing line of the G2 and G4 the minimum of energy is located at

{q

m e

=

−ΔGprot + Fη + λe 2λe

The striking observation in the above two results is that the electron-transfer coefficient for the concerted pathway α14 is independent of ΔGprot. To make this more explicit, we will rewrite the above at the limit of small overpotential η ≈ 0 and use the definition of ΔGprot from eq 10.

‡ ΔG24 = G2(qem , qpm) − G2(0, 1)

(ΔGprot − Fη + λe)2 (21)

Similarly, at the crossing line of G1 and G4, the minimum

{q

m e

= qpm =

Fη + 2λ ̅ + λe + λ p 2(2λ ̅ + λe + λ p)

} and the

corresponding transition state energy relative to the minimum of G1 is (see SI for the details) ‡ ΔG14 = G1(qem , qpm) − G1(0, 0) =

∂ΔG‡ ∂(Fη)

(28)

pHtrans

α24 =

−(ΔGprot) + Fη 2λe

+

1 2

2⎞ ⎛ 1 ⎜ (Fη + 2(λ ̅ ) + λe + λp) ⎟ = ⎟ + pK a 2.3RT ⎜⎝ 4(2λ ̅ + λe + λp) ⎠

(29)

Note that while the pHtrans depends on the pKa of the surface, they are not the same, as implied by the first term in the above equation. Finally, Figure 3 graphically represents the PES for select values of parameters. The variation of α as a function of pH can be understood from this Figure in a relatively intuitive way. First, it is noted that at the high-pH limit (Figure 3a) the transition state is in the middle of the PES and the G2 corner is raised significantly higher than that. Under this condition, a small change in the height of G2 (i.e., pH) will not influence the saddle point height. The overpotential will change the relative heights of the G1 and G4 states and hence will influence the height of the transition state that is at their crossing point. Consequently, the transition-state energy will be sensitive to

(23)

Fη 1 + 2(2(λ ̅ ) + λe + λp) 2

2 ⎛ ⎞ 1 ⎜ (Fη + 2(λ ̅ ) + λe + λp) + G(M) − G(MH+)⎟⎟ ⎜ 2.3RT ⎝ 4(2(λ ̅ ) + λe + λp) ⎠

which based on the ΔGprot = 0 (eq 10) for the point of protonation equilibrium can be written in terms of surface pKa as follows:

4(2λ ̅ + λe + λp)

Using the above, we arrive at the following two expressions for the electron-transfer coefficient for the two transition states α14 =

(27)

(Fη + 2λ ̅ + λe + λp)2

PREDICTION OF THE MODEL FOR THE PH DEPENDENCE OF α We will use the formal definition (ref) of the electron-transfer coefficient as the sensitivity of the transition state to the applied overpotential2 α=

−G(MH+) + G(M) − 2.3RT pH 1 + 2λe 2

pHtrans =

(22)

■

α24 =

2λe

sition-state energy relative to the minimum of G2 is

energy is located at

(26)

imentally verifiable. As explained before, the model also predicts that at high pH the concerted path 1 → 4 is preferred because protonation of the surface is unfavorable, while at low pH the stepwise path 1 → 2 → 4 becomes favorable. Thus an experimental test of this model will require measuring α for a range of pH values and studying its pH dependence at highand low-pH limits. The experimental work that is presented in the next section was motivated by this hypothesis. While we will show results that partly agree with this hypothesis, we will also discuss the experimental impediments and nuances that interfere with the measurement of α and can deter from unequivocal verification of this model. The model also predicts the transition pH, lower than which the stepwise and higher than which the concerted mechanism is at play. The pHtrans may be estimated by setting the minimum of the G2 surface (eq 13) equal to the energy of the 1 → 4 transition state (eq 22). At that point, accessing the minimum of G2 from the minimum of G1 will require the same free energy as accessing the 1 → 4 transition state. The pH value that achieves this is found to be

} and the corresponding tran-

4λe

1 2

Thus the model presents a pH-independent α for the concerted path and a pH-dependent α for the stepwise path. More specifically, the negative sign of the pH term in the eq 27 means that a decrease in pH should increase α with a linear slope of 2.3RT . These predictions are, in principle, exper-

, qpm = 1

= −ΔGprot + Fη +

α14 =

(24)

(25) D


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variations in onset potential and total current, we first concentrate on the common features observed in all of the electrodes. The features that are common to all electrodes are the following. From both the I(pH,E) graphs and the α(pH,E) plots (Figures 4 and 5) two distinct regions in pH with different behavior are identifiable. At higher pH values the overpotential is clearly larger while the empirical α is smaller and somewhat pH-independent. At lower pH values a smaller overpotential is observed with linear dependence on pH, which is close to the Nernstian slope for some of the electrodes. The value of α is distinctly larger in the acidic region compared with the basic region. It also shows a linear increase with decreasing pH value for many of the electrodes in the acidic range. The high- and low-pH regions seem to have an abrupt transition pH in the range of 2.5 and 4. At large overpotentials, corresponding to large currents, the empirically determined α becomes small and nearly vanishes, pointing to mass-transfer limitations on the rate. It should be noted that whenever the current becomes mass-transfer-limited the empirical electron transfer can no longer be interpreted as α = −(2.3RT/F)(∂ log I/∂E). For that reason, it is most reasonable to only concentrate on the value of α for low values of current, corresponding to the current onset edge in the I(pH,E) plots. A convenient way to see the variation of alpha as a function of pH is to isolate the average value of α near the onset for each pH value, as discussed in the Methods section. In Figure 6a,b, we show the variation of α as a function of pH for several electrodes. The overall observation in Figure 6a,b is that α rises with decreasing pH at low-pH range and is nearly constant at high-pH range. Two observations in the data are interestingly similar to the predictions of the model discussed above and shown in Figure 6c. The first is the existence of two regions, the high- and low-pH regions, with distinct kinetic behavior. The second is the nearly constant value of α for the high-pH region and the linearly increasing α with decreasing pH in the low-pH region. Figure 6 shows the qualitative

Figure 3. Free-energy surfaces for CPET (a) and stepwise paths (b). The transitions states are indicated by *. As explained in the text, pH controls the height of the surface in the corner 2. At high pH, protonation is unfavorable, corner 2 is raised, and the PES shown in (a) determines the reaction. At low pH, protonation is spontaneous, corner 2 is lowered, and the PES shown in (b) controls the reaction.

the overpotential (α ≠ 0), but it will be insensitive to pH. In the low-pH limit (Figure 3b), the height of G2 is significantly lower compared with the saddle point and proton transfer is spontaneous. In that situation, the transition state is along the electron-transfer coordinate and will be sensitive to the relative heights of G2 and G4. The height of G2 is controlled by both potential and pH (eq 13). Thus the transition state will be sensitive to overpotential (α ≠ 0) and will also be pHdependent.

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RESULTS AND DISCUSSION To emphasize both the pH and potential dependence of the electrochemical rate, we present our results in 2D plots of current as a function of pH and potential I(pH,E), which have been named dynamic potential−pH diagrams (DPPDs).27,28 Figure 4 a−g shows such measurements. The electron-transfer coefficient α is presented in the form of contour plots α(pH,E) for different types of electrodes in Figure 5. We chose a variety of electrodes to find out if the pH dependence of α varied for different materials. While different electrodes do show

Figure 4. Electrochemical current logI(pH,E) for hydrogen evolution reaction on the surface of different electrodes as a function of pH and potential (a) Pt, (b) Au, (c) Cu, (d) Ni, (e) Ti, (f) FeS2, and (g) glassy carbon (GC). The color scale is kept the same in all figures for ease of comparison. The Pourbaix line for water stability (solid line) is overlaid for reference. As expected, Pt exhibits almost no overpotential (the potential difference between the Pourbaix line and the onset of current) at low-pH values, while GC has the highest overpotential in the same range. E


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Figure 5. Measured electron-transfer coefficient α(pH,E) for Pt, Au, Cu, Ni, Ti, FeS2, and glassy carbon (GC) electrodes. The color scale is kept the same in all figures for ease of comparison.

Figure 6. Experimentally measured values of α as a function of pH for different type of electrodes (a) copper, gold, platinum, and iron pyrite. (b) Glassy carbon, nickel, and titanium. The two sets of data are shown separately for clarity. (c) Calculated values of α as a function of pH, which is obtained from the model for selected values of parameter: η14 = −0.4 V, η24 = −0.1 V, λe = λp = 0.2 eV, λ̅ = 0.15 eV, and pKa = 3.

the electrode can be maintained and mass-transfer limitation can be partially mitigated. To find out how rotation influences the behavior described so far, we performed the experiments for three electrode materials, gold, platinum, and glassy carbon, for which we had suitable RDEs available. The results of the RDE experiments are shown in Figures S3−S5 of the SI. An important observation is that the apparent transition pH values seen in the experiments performed without rotating electrode (Figures 4 and 5) move to higher pH values upon rotation. This dependence on rotation speed indicates that the apparent transition pH, which was pointed out earlier as one of the inconsistent points between the model and the experiment, is a function of mass transfer. A series of models, such as the Levich equation, systematically relate the rate to rotation speed. We have found that in the transition region the current correlates with the Levich equation to some extent (see SI). Thus we suggest that while mass transfer may be a factor that influences the value of the apparent transition pH, an underlying chemical mechanism may still be at play. In other words, we hypothesize that even if mass-transfer limits are entirely removed the kinetic parameters at basic pH values would be distinctly different from those at acidic pH values and the reaction would follow the PES described before. To isolate the effects of mass transfer, further

similarity between the experimental data and the predicted trend based on the model. Reporting this similarity is an important message of our work. However, there are several features in the data that do not seem to plausibly follow from the model. First is the similarity in the transition range of pH for various types of electrodes. The model predicts the transition pH to depend on the surface pKa, as shown in eq 29. Because the surface pKa of different materials are expected to be different, the transition pH should vary for different electrodes. The data, on the contrary, show a narrow range of pHtrans 2.5−4 for all of the electrodes studied. This aspect of the findings contradicts the model. Neglect of mass-transfer considerations may be the source of this discrepancy. Mass-transfer limitations influence the measurement of electrochemical rates. In particular, at high overpotentials the rate becomes large enough that the concentration of reactants and products near the surface largely deviates from those of the bulk. Thus at large current values the value of pH near the surface will be markedly more basic compared with that of the bulk. The known technique to understand and isolate the influence of mass-transfer limits on the rate is the RDE method.33,34 At high rotation speeds, a larger flux of material to F


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(4) Jiao, X.; Batchelor-McAuley, C.; Kätelhön, E.; Ellison, J.; Tschulik, K.; Compton, R. G. The Subtleties of the Reversible Hydrogen Evolution Reaction Arising from the Nonunity Stoichiometry. J. Phys. Chem. C 2015, 119, 9402−9410. (5) Durst, J.; Siebel, A.; Simon, C.; Hasche, F.; Herranz, J.; Gasteiger, H. A. New Insights into the Electrochemical Hydrogen Oxidation and Evolution Reaction Mechanism. Energy Environ. Sci. 2014, 7, 2255− 2260. (6) Schmickler, W.; Santos, E. Interfacial Electrochemistry; Springer: Berlin Heidelberg, 2010. (7) Sheng, W.; Gasteiger, H. A.; Shao-Horn, Y. Hydrogen Oxidation and Evolution Reaction Kinetics on Platinum: Acid vs Alkaline Electrolytes. J. Electrochem. Soc. 2010, 157, B1529−B1536. (8) Devanathan, M. A. V.; Stachurski, Z. The Mechanism of Hydrogen Evolution on Iron in Acid Solutions by Determination of Permeation Rates. J. Electrochem. Soc. 1964, 111, 619−623. (9) Zheng, Y.; Jiao, Y.; Jaroniec, M.; Qiao, S. Z. Advancing the Electrochemistry of the Hydrogen-Evolution Reaction through Combining Experiment and Theory. Angew. Chem., Int. Ed. 2015, 54, 52−65. (10) Norskov, J. K.; Bligaard, T.; Logadottir, A.; Kitchin, J. R.; Chen, J. G.; Pandelov, S.; Stimming, U. Trends in the Exchange Current for Hydrogen Evolution. J. Electrochem. Soc. 2005, 152, J23−J26. (11) Greeley, J.; Jaramillo, T. F.; Bonde, J.; Chorkendorff, I.; Norskov, J. K. Computational High-Throughput Screening of Electrocatalytic Materials for Hydrogen Evolution. Nat. Mater. 2006, 5, 909−913. (12) Jaramillo, T. F.; Jørgensen, K. P.; Bonde, J.; Nielsen, J. H.; Horch, S.; Chorkendorff, I. Identification of Active Edge Sites for Electrochemical H2 Evolution from MoS2 Nanocatalysts. Science 2007, 317, 100−102. (13) Conway, B. E.; Bockris, J. Electrolytic Hydrogen Evolution Kinetics and Its Relation to the Electronic and Adsorptive Properties of the Metal. J. Chem. Phys. 1957, 26, 532−541. (14) Parsons, R. The Rate of Electrolytic Hydrogen Evolution and the Heat of Adsorption of Hydrogen. Trans. Faraday Soc. 1958, 54, 1053−1063. (15) Trasatti, S. Work Function, Electronegativity, and Electrochemical Behaviour of Metals. J. Electroanal. Chem. Interfacial Electrochem. 1972, 39, 163−184. (16) Conway, B.; Tilak, B. Interfacial Processes Involving Electrocatalytic Evolution and Oxidation of H2, and the Role of Chemisorbed H. Electrochim. Acta 2002, 47, 3571−3594. (17) Marković, N. M.; Grgur, B. N.; Ross, P. N. TemperatureDependent Hydrogen Electrochemistry on Platinum Low-Index Single-Crystal Surfaces in Acid Solutions. J. Phys. Chem. B 1997, 101, 5405−5413. (18) Sheng, W.; Gasteiger, H. A.; Shao-Horn, Y. Hydrogen Oxidation and Evolution Reaction Kinetics on Platinum: Acid vs Alkaline Electrolytes. J. Electrochem. Soc. 2010, 157, B1529−B1536. (19) Sheng, W.; Zhuang, Z.; Gao, M.; Zheng, J.; Chen, J. G.; Yan, Y. Correlating Hydrogen Oxidation and Evolution Activity on Platinum at Different pH with Measured Hydrogen Binding Energy. Nat. Commun. 2015, 6, 5848. (20) Shinagawa, T.; Garcia-Esparza, A. T.; Takanabe, K. Mechanistic Switching by Hydronium Ion Activity for Hydrogen Evolution and Oxidation over Polycrystalline Platinum Disk and Platinum/Carbon Electrodes. ChemElectroChem 2014, 1, 1497−1507. (21) Strmcnik, D.; Uchimura, M.; Wang, C.; Subbaraman, R.; Danilovic, N.; van der Vliet, D.; Paulikas, A. P.; Stamenkovic, V. R.; Markovic, N. M. Improving the Hydrogen Oxidation Reaction Rate by Promotion of Hydroxyl Adsorption. Nat. Chem. 2013, 5, 300−306. (22) Auinger, M.; Katsounaros, I.; Meier, J. C.; Klemm, S. O.; Biedermann, P. U.; Topalov, A. A.; Rohwerder, M.; Mayrhofer, K. J. J. Near-surface Ion Distribution and Buffer Effects During Electrochemical Reactions. Phys. Chem. Chem. Phys. 2011, 13, 16384−16394. (23) Grimminger, J.; Schmickler, W. Dynamics of Combined Electron- and Proton Transfer at Metal Electrodes. Chem. Phys. 2007, 334, 8−17.

experiments along with models that potentially go beyond the diffusive assumptions of the Levich equation are possibly necessary.

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CONCLUSIONS We have analyzed a parametrized PES for the reduction of one proton (Volmer reaction) which is based on the work of Schmickler and Koper. The influence of pH on the geometry of the PES and possible reaction pathways has been thoroughly discussed. We calculated the electron-transfer coefficient α based on this model and evaluated its pH dependency. We showed experimental results on the variation of empirical α for hydrogen evolution reaction on different types of electrodes over a wide pH range. There are several similarities between the pH dependence of α derived from the model and the empirical α based on the experiments. The data suggest that the governing mechanisms may be stepwise proton−electron transfer in the low-pH and CPET in the high-pH range. We caution that the similarity between the observations and the model should not be taken as proof of the model. Some features of our data are not fully explainable by the prediction of the model such as the transition pH between the acidic and basic region. We hope that our work can inspire further theoretical and experimental studies on understanding proton thermodynamics and kinetics near an electrode. In particular, theoretical work on explicit pH dependence of the transfer coefficient is desirable. Also, new experimental approaches and models that will isolate the mass-transfer effects and concentrate on local spectroscopic measurements on the surface are expected to be useful in further elucidation of this problem.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b10602. IR compensation, transition state derivation, and HER analysis using RDEs. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 213-740-9337. ORCID

Jahan M. Dawlaty: 0000-0001-5218-847X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support from the University of Southern California startup grant, the AFOSR YIP Award (FA9550-13-10128), and the NSF CAREER Award (1454467).

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REFERENCES

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pH Dependence of the Electron-Transfer Coefficient: Comparing a

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